Play free slots now. 
Vegas Basics
Vegas Bargains
How to play the games
All about Slot Machines
Gambling 101
Gambling 102
Online Gambling

Reason #4 like Bovada:

It's fair and safe

Online gambling is largely unregulated in the U.S.  That means the casinos serving U.S. players generally don't answer to anyone.  If you have a problem with a casino (like they won't pay you), then you're usually out of luck.  I can't count how many players have written to ask me for help because they didn't get paid by some other casino.  (Not that I helped them—if a dodgy casino won't pay you then you're on your own.)

That's why the most important thing in playing online is to pick a good casino.  The good ones know they make more money with fair games and consistent payouts, because that ensures repeat customers and good word-of-mouth referrals.  It's no coincidence that the most successful online casinos are the ones that focus on their customers.

But some casinos aren't so smart.  The stupidest ones actually rig the games, promptly get blacklisted at sites like Casinomeister, and then their business dries up.  (It's pretty easy for watchdog mathematicians like the Wizard of Odds to determine whether a casino is cheating.)

Cheating is rare.  You're more likely to have a problem getting a payout.  Some casinos try to find excuses to not pay winning players, especially players who have won big.  And again, since online gambling is unregulated in the U.S., if you can't get a payout from a casino, then you're usually out of luck.

So all this is another reason why I advertise Bovada, and have done so for over ten years.  They use industry-standard software, it's absolutely fair, and players get their payouts, consistently.  I have a choice in whom I advertise, so I purposefully picked a casino with a good reputation where I'm confident my readers will have a good experience.

To be clear, Bovada's not perfect.  Once they got duped by a vendor (Betsoft) who provided progressive slots whose jackpots weren't winnable.  When I discovered this I alerted Bovada, and they pulled all the Betsoft games from the site, but I thought they were slow to do so and didn't offer proper restitution to affected players.  Still, even with this incident, their overall history is better than most; as just one example, there are many other casinos still offering Betsoft's questionable games.

Another good thing about Bovada is that they allow me to mediate if one of my readers clicks over to them, plays the games, and has a problem they can't get Bovada to resolve.  Believe me, I wouldn't offer that service if I got more than a trivial number of inquiries over the years on that topic.

Bottom line: I'm confident that Bovada is fair and safe.  You might have a good experience with another casino...and you might not.  I trust Bovada, and that's why I picked them.

Visit Bovada


Gambling problem?
  1. Call the 800-522-4700 hotline or get online help
  2. See these horror stories.
  3. Know that Parkinson's drugs encourage gambling.
Play these
free slots now

Gambling problem?
  1. Call the 800-522-4700 hotline or get online help
  2. See these horror stories.
  3. Know that Parkinson's drugs encourage gambling.

Exposing the Gambler's Fallacy

October, 2018.

You're playing roulette, and red has just come up eight times in a row!  Now's the time to bet on black, right?  Wrong.  Red and black are equally likely.  Even though we've just seen a bunch of reds.  How can this be?  Let's find out.

The gambler's fallacy is the mistaken belief that some result becomes more likely (or less likely) because of what happened before.  The reality is that the odds don't actually change.  Here are some examples.

  1. MYTH:  In craps, if seven hasn't come up for a while, it's about to come up because it's "due".
    REALITY:  Nothing is ever "due" in a random game.  Seven is equally likely on every roll, regardless of how long the dry spell has been.

  2. MYTH:  Once someone hits a slot machine jackpot, that machine becomes less likely to hit a jackpot for a while.
    REALITY:  Every spin has an equal chance of hitting the jackpot, regardless of whether the last jackpot was hit recently or thousands of spins ago.

  3. MYTH:  The next ten spins in roulette are more likely to be R R b R b b b R b R than ten reds.
    REALITY:  Each is equally likely.  I know, this one is hard to wrap your head around.  We'll get to that one in the discussion below.

Let's see why the fallacy seems to be right, and why it's actually not.  We'll use coin flips because they're easy to understand.

We'll start with two things you already know:  the chances of getting heads on a single coin flip is 1/2, and it's unlikely you'll get a bunch of heads in a row.  For example, here are the chances of getting ten heads in a row:

  x    x    x    x    x    x    x    x    x    = 

That's 1 in 1,024.  Not very likely, of course.

So here's where the gambler's fallacy comes in:  Say you've tossed the coin nine times and amazingly, you got nine heads. You figure that the next toss will be tails, because the probability of getting ten heads in a row is one in 1024, which is really unlikely to happen.

The problem with this reasoning is that you're not looking at the chances of getting ten heads in a row, you're looking at the chances of getting one heads in a row.  The heads that already happened no longer have a 50% chance of happening, they already happened.  When you flip again the odds for that flip will be 50-50, same as it ever was.

Let's introduce our hero, Mr. P ("P" for "probability").  He'll always be looking to the future to see what's going to happen.  Here he's about to make ten coin flips, hoping to get ten heads.  Here's his outlook:


Mr. P, lucky guy that he is, got nine heads in a row.  Here he is, getting ready to make his tenth flip:

Now you're saying, Hey, wait! How come all the 1/2's turned into 1's?  The answer is that they're no longer unknowns.  Before you flip a coin you don't know what's going to happen so you have 50-50 odds.  But after you flip the coin you definitely know what happened!  After you flip a coin, the probability that you got a result is 1.  You definitely flipped the coin.  Definitely, definitely.  So after you've flipped nine heads, the probability of flipping a tenth head is 1x1x1x1x1x1x1x1x1x 1/2 = 1/2.

Let's have another look at Mr. P:

Notice that it doesn't matter where on the line you stick him, the chances of his next flip being heads is always 1/2.  Wherever he is, it doesn't matter what happened before, his chances on his next toss are always 1 in 2.

How could it be otherwise?  When you flip a coin you will get one result out of two possible outcomes.  That's 1 in 2, or 1/2.  Why and how could those numbers change just because you got a bunch of heads or tails already?  They couldn't.  The coin has no memory, it neither knows nor cares what was flipped before.  If it's a 1-out-of-2 coin, it will always be a 1-out-of-2 coin.

Still not convinced?  Then here's another way to think about it:  Let's say someone hands you a coin and asks, "What are the chances of flipping heads?"  Without hesitation you'd probably say 1 out of 2?  But wait a minute—if it were true that heads were more likely if tails has just come up a bunch of times, then why did you answer "1 in 2" right away when asked about the chances of getting heads?  Why didn't you say, "Well, first you have to tell me whether tails has been coming up a lot before I can tell you whether heads has a fair shot or not."?  It's simple: You didn't ask about the previous flips because intuitively you know they're unimportant.  If someone hands you a coin, the chances of getting heads are 1 in 2, regardless of what happened before.

Would it really be the case that you answered "1 in 2," and then your friend said, "Oh, I forgot to tell you, tails has just come up nine times in a row." Would you now suddenly change your answer and say that heads is more likely?  I hope not.

One last example:  Let's say your friend slides two quarters towards you across the table.  She tells you that the first coin has been flipping normally, but the second quarter has just had nine tails in a row.  Would you now believe that the chances of getting heads on the first coin are even but the chances of getting heads on the second coin are greater?  Given two identical coins, could you really believe that one would be more likely to flip heads than the other?   I hope not!

The same concept applies to roulette.  An American roulette wheel has 18 red spots, 18 black spots, and 2 green spots.  The chances of getting red on any one spin are 18/38.  If you just saw nine reds in a row, what is the likelihood of getting black on the next spin?

18/38, same as it ever was.


The casino is playing you

Casinos are only too happy for you to buy into the gambler's fallacy.  That's why they put an LED marquee on the roulette table showing what numbers have hit recently, and why they give baccarat players pads and pencils to track the results.  They're not afraid to do that because they know that tracking what happened before is completely useless.  Come on, are the casinos really gonna help you win?!  Of course not.  The fact that they're willing to help you track results should be an obvious red flag.  They're hoping you fall for the fallacy and play longer, trying to chase a non-existent streak.  Forewarned is forearmed.  Don't fall for it!


Why R R b R b b b R b R in roulette is just as likely as ten reds

Here's a typical example of someone getting sucked into the gambler's fallacy because it seems reasonable.  This was a post on an online gambling forum:

"Another example to show how useless those mainstream gambling math theories are is that first they claim that all even money bets have equal odds, and then the very same math 'gurus' claim that this sequence: R R R R R R R R R R  has equal probability with this: R R b R b b b R b R.  The first statement contradicts the second and it's very obvious.  Thus there is a serious flaw in your perception.  I suggest you to reconsider from scratch all those mainstream and generic probability theories because they have no value in action but only on papers." (source)

Hey buddy, I just report the laws of math, I don't make them, okay?  And by the way, these aren't "theories", as in unproven ideas, they're ironclad fact.

The mixed pattern of reds and blacks seems more likely.  Because normally when you play that's what you see: a mixed pattern of reds and blacks.  You almost never see ten reds in a row.  So, because you normally see mixed reds and blacks, our critic figured that getting that pattern of mixed reds and blacks is way more likely than ten reds.

The problem is that our critic chose a specific pattern of reds and blacks.  Any specific pattern of ten mixed reds/blacks is just as likely as ten reds.  Going through the pattern, what's the chance of getting the first red?  It's 1/2, of course.  How about the second red?  Also 1/2.  For the third result, black, what are the chances?  Again, 1/2.  And so on.  It doesn't matter whether our result is supposed to be red or black, the chances of either one are 50-50.  You multiply out those ten 50-50 chances, your results are 1 in 1024, no matter whether the pattern is RRbRbbbRbR, RRRRRRRRRR, bbbbbRRRRR, or anything else.

To prove this, I programmed a simulator, below.  It spins a bunch of times and tells you how often each pattern came up.  Go ahead, try it.

Chances of Unique Patterns in Roulette
(excluding green 0/00)
Pattern
Number of Sessions
What it shows is that the pattern is no more likely than the same number of reds in a row.  (If your test showed otherwise, that's because there's some variance after only 100,000 spins.  Run it again.)

The first set of results is for a bunch of sessions with exactly as many spins as is in the pattern.  If you've been following along, you probably won't be surprised that the chances for our pattern are the same as for a bunch of reds in a row.

The second set of results treats all the spins as a single huge session.  Here again, the mixed pattern and the all-reds pattern have the same chances.

The third set is why our critic got snookered by the fallacy.  It shows that a set of ten mixed reds/blacks is way more likely than ten reds.  Our critic thus thought that this meant that his specific pattern of reds/blacks was more likely than ten reds, but that's not the case.  Once you have a specific pattern, the chances are the same as for ten reds.  The simulator proves it.